Screw modifier counterclockwise?
Taking some information from the comments:

You have at least two ways to do this.


Option 1: Duplicate the object, and set the Angle on the new object to a negative value.
Option 2: Add a Mirror modifier after the Screw modifier (just one object here).


Note that with either of these, you may end up with Z-fighting at the points where the two wraps intersect.